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Abstract

We demonstrate optical manipulation of structures and defects in liquid crystals (LCs). The effective refractive index depends on the LC molecular orientations and the laser beam’s polarization. We use the orientation-mediated refractive index contrast for the laser trapping in LCs with a homogeneous composition, but with spatially-varying patterns of molecular orientations. Tightly-focused polarized beams allow for optical trapping of disclinations and their clusters, dislocations and oily streaks, cholesteric fingers and focal conic domains, etc. We calculate the optical gradient forces for typical structures and explain the trapping properties at low laser powers. We also show that when a high-power beam causes local molecular realignment, the laser trapping properties change for two reasons: (1) the refractive index pattern and optical gradient forces are modified; (2) additional elastic structural forces arise to minimize the elastic free energy.

Figures (7)

Figs. 1. (a). − 1(c). Polarizing microscopy textures: (a) domains with a uniform (left) and the 180° -twisted across a cell director (right); (b) cholesteric fingers in a homeotropic cell; (c) toric focal conic domains in a smectic LC. (d-f) Director fields in vertical cross-sections of the structures: (d) for a wedge cell shown in (a) with a disclination line separating the two domains; (e) for a cholesteric finger of the CF3 type; (f) for the toric focal conic domain. The defect lines in (d-f) are marked by the red lines or filled circles. Note that four different types of cholesteric fingers are known [34], and (e) illustrates the simplest one. Crossed polarizers in (a-c) are along the vertical and horizontal image edges.

Fig. 2. Optical manipulation of cholesteric CDs: (a, 2 MB) video sequence and [Media 1] (b-e) extracted images. Using a single beam that is time-shared between four traps, four CDs (marked by white arrows in (a)) are first positioned in vertices of a square and then are set to follow computer-programmed concentric motion trajectories as shown in video frames (a-e) taken at about 1s time intervals. (f) The director structure of the CD in the plane of the LC cell. Textures (a-e) were obtained with the crossed polarizer and analyzer along the image edges. The black ellipses in (f) mark the two equally-possible trapping cites for large CDs when the trap’s linear polarization is along the horizontal direction (marked by the black bar and “P”).

Fig. 3. Stretching of an optically trapped dislocation in a lamellar LC by moving the sample using a stage: (a, 1.1 MB) video sequence and [Media 2] (b-g) extracted representative image frames. The directions of the sample displacement are shown by the black arrows in (a-g). (h) Layers profile in the vertical FCPM cross-section that was obtained (before the optical trapping experiments) in the plane orthogonal to the dislocation, as shown by the h-h line in (d). Schematics of the director field around the defect core shown by the red circle in (h). Linear polarization direction of the trapping laser beam is along the y-axis in (a-g). FCPM polarization direction in (h) is along the defect line. Polarizing microscopy textures (a-g) were obtained with the crossed polarizer and analyzer along the vertical/horizontal image edges.

Fig. 4. Laser manipulation of a disclination quadrupole: (a, 1.9 MB) video sequence and [Media 3] (b-f) extracted frames. A single beam is time-shared between the two IR traps visualized in (a) by a HeNe laser beam co-localized with the trapping beam. The traps are slowly shifted as shown by white arrows in (a) and the disclinations are stretched (a-f) until they escape from the traps (f), because of their line tension. (g) Layers structure visualized by the FCPM for the vertical cross-section perpendicular to the cluster, as marked by the g-g line in (b). (h) The director field around the disclination cluster shown by the red circle in (g). Linear polarization of the laser beam used for manipulation is along the y-axis in (a-f). FCPM polarization direction is normal to the image and along the cluster in (g). Textures (a-f) were obtained with the crossed polarizer and analyzer along the image edges.

Fig. 5. (a). An image showing that a linearly-polarized beam of powerW ≈ 100mW exerts torsion and locally reorients an initially straight disclination cluster shown in Figs. 4. (b), 4(c) Schematics of the molecular alignment in the central part of (b) the undistorted cluster [similar to that shown in Fig. 4(h)] and (c) with the local laser-induced director reorientation that results in the structure trapping at high powers, as shown in (a). Crossed polarizers are along the image edges in (a).

Fig. 6. Models of the LC structures and the calculated optical gradient forces. (a) A semi-infinite domain (SID) of thickness lz extending from x=0 (thick lines in (a)) to infinity ∞ along the x-axis and from −∞to ∞ along the y-axis.(b) A stripe-like domain (SD) of thickness lz width lx and extending from −∞ to ∞ along the y-axis. (c) A domain with finite dimensions. (d-f) Calculated gradient forces vs. the distance to the trap’s center: (d) for the structures shown in (a) using Eq.(6); (e) for the SD fragment using Eq.(4) and sizes marked on the figure; (f) for the structure shown in (c) using Eq.(2) and the marked sizes l = lx=ly =lz. We used W = 15mW and indices marked in (d) in calculations for the SID. Indices nDS = 1.55,nSLC = 1.47 were used in the calculations for the SD and the cubic domain in (e,f).

Fig. 7. Optical gradient forces calculated for the cholesteric CD and for power W = 15mW . The values of pitch p are marked for each curve. The trapping positions (zero force) are shown by the arrows. Note that large CDs can be trapped at a finite distance from their center.